Woodward — The Efficiency of Gearing under Friction. 103 

 The energy exerted by the driver during this action is 



UmH-M, 



and the ratio of energy lost to energy exerted is 



li 



- ^1 + ^2 .. / 1 | 1 



\*q-h log (l +|J-A'l0g(l+|)j (15). 



Let n 2 and n 2 represent the numbers of teeth in the driver 

 and follower. Then, but one pair of teeth being in action at 

 a time, 



_ 7rr i 

 9 ~~^' 



When the obliquity is as small as possible, 



max. r = q sin 6 = r x cos 



hence tan 6 = - 1 = -> and 



(£ 7T 



. sin (0 — <p) . . a . n, — irf 



h = r, . \ . r/ = r, ( cot cp — cot 0) = r. -3 — — £ 

 1 sm 6 sin 9? 1 -. r y ■ w,/ 



h' = r, . \ . r/ = r, (cot <p + cot 0) = r, -3 — -^ 

 1 sin sin (p ' v T y l n x f 



Vr 1 T r f /2y 1 U/ n^tt^ 



Substituting the above values in (15) and removing r x from 

 the brackets, we have 



R = - + - oH — — - — ^ log ( 1 + — —J 



ra i/ V n, + 7T/7 



